Friday, May 10, 2013

Scientific Truth and the Nature of Mathematical Inquiry

Today I heard that proving the efficacy of the technique called "forcing" in set theory is made much more elegant and clear by the assumption of Platonism.

So what? I hear you ask.

So... so everything.
Scientific truth is determined by a variety of criteria, but some quite important ones are practical utility and elegant descriptive power. I think everyone who understands any scientific field can agree that mathematics is of significant practical utility, and set theory is immensely useful within mathematics. In some scientific sense then, the philosophical assumptions underlying set theory are true.

I feel I need to justify the reliance on elegant descriptive power more than simply citing it (paraphrased) as one of the criteria by which scientific theories should be judged mentioned in The Grand Design by Stephen Hawking and Leonard Mlodinow, so here goes. Occam's razor warns us to not multiply entities beyond necessity, but this principle naturally extends itself to a broader view of complexity, namely that one should generally choose "simpler" explanations in place of more "complicated" ones, for some reasonable definitions of those terms. The reason I attribute this to elegance, particularly in the metamathematical use of the term, is exemplified by the original "revolution":
Copernicus did not actually "prove" that the motions of the planets are those of massive spheroids orbiting the sun, he did not demonstrate that the preceding system of calculation using epicycles was actually incorrect per se, what he proved was that the heliocentric model provides a much more mathematically elegant description of their motion. Technically everything which can be calculated using the Copernican system can also be calculated using epicycles, but it is much more intricate and difficult to do so, leading to the worldwide scientifically-minded community naturally adopting the view that Copernicus' model of the motion of the planets is in some important sense closer to the truth.

Apparently certain important proofs in set theory (at least the efficacy of forcing) are made more elegant by assuming a Platonic view of first-order set theory - by this I mean assuming that there is some part of reality which set theory describes to some degree of accuracy, and that the practice of set theory is in some way the apprehension of this part of the external reality. As I take a materialist view of reality this assumption is quite incompatible with the way I have so far dealt with mathematics on a philosophical level.

Anybody who is familiar with the dialogue of mathematicians will know that we all tend to speak as though the objects we are discussing are in some sense external to ourselves, that there are "real truths" to be discovered. I have thought of this as largely a reasonable way to speak about it for three reasons.
1) It is a very useful shorthand.
2) In a sense it is true no matter which view of the subject the speaker takes.
3) The culture of mathematicians has formed with this mode of speech built into it, so to participate in the mathematical culture one must first adopt some of its basic mannerisms.
All of these reasons are perfectly valid for a materialist and do not at all rely on the objects of study existing in some actual realm of Platonic ideal forms. In particular my own view is that mathematics is a description of the subjective experience of precise comprehension shared by all human(-like) minds (roughly speaking - it's an idea I find difficult to put into words).
However when Kurt Gödel proved his incompleteness theorems the philosophical question of what mathematics is actually describing (if anything) was dropped squarely into the core of the foundations of math, of which set theory is an important part. To describe why this philosophical question suddenly became significant in philosophy of math would likely be redundant to mathematicians (and philosophers of math and logicians) and merely confusing to everyone else, so I will forego a review of the history of this area here.

Now while it is arguable whether or not mathematics is a science at all (I would argue against that proposition) it is certainly a discipline with immense practical utility. I hope I don't need to say anything here to justify that statement, so I will continue without doing so. Set theory is important within the practice of mathematics, in part because I have yet to encounter a mathematical subdiscipline which does not occasionally make use of some of its more basic results. Suffice it to say that if set theory were to crumble it would seriously threaten to take most if not all of mathematics with it. Set theory, I have now heard, is noticeably more complicated and nuanced when working without the assumption of Platonic reality. Obviously (to me, anyway) this assumption, being a philosophical rather than a mathematical one, does not affect the actual mathematical content of the results of set theory, but it may still affect their phrasing and thereby their apparent applicability outside of math itself. To me this is reminiscent of the row between constructive and classical logics; that ultimately the mathematical community decided that since results could be equivalently phrased in either logical system constructive logic, being somewhat unwieldy, was to be considered redundant, effectively granting victory to the side of classical logic. This conclusion of the fight between constructive and classical logics is another instance of the more elegant theory being considered closer to the truth in virtue of its elegance.

So it seems that some metascientific methodologies tend to be applied within philosophical questions of metamathematics at least, and the results can then be widely accepted as "true" in some real but non-mathematical sense, and their use throughout the scientific disciplines lends the philosophical assumptions underlying mathematics seemingly as much claim to "truth" in the external world as the physical sciences themselves can claim. Directly applying this approach to the assumption of Platonism in set theory (as it results in a more elegant set theory, it can be assumed to be true in a scientific sense), we reach the conclusion that a platonic realm of ideal forms (consisting at least of sets) provisionally likely exists as a part of objective reality. This obviously contradicts philosophical naturalism, but more interestingly (and confusingly) it also can be seen that the existence of this nonmaterial realm of Platonic ideal forms has been arrived at using scientific principles of decision-making, which also contradicts the idea that science is methodologically naturalistic.

So has methodological naturalism reached a decidedly non-naturalistic conclusion, even provisionally?

I suppose we add this to Lawrence Krauss' paradoxical conclusion that empirical rationalism tells us that at a future time empirical rationalism will correctly reach a false conclusion.

Friday, February 26, 2010

Painful Silence

Phone calls and emails about my grandfather over the course of a week - something about pneumonia, but they say he'll pull through soon enough. He's been hinting about wanting do die for about a year now, so I'm not so sure. I give him a call and he seems happy enough to hear from me, but he also sounds slightly high, I guess it must be the morphine, but I say nothing.

A couple of days later I get a call saying that something's gone wrong, he probably won't pull through so they're taking him off the medicine and allowing him to die. He's had a DNR for a long time now, so this is a simple matter. We'll be leaving in two days to go see him before he dies.

Long car trip, short bursts of conversations I don't remember, and short stretches of silence as well. We arrive and say hello, he seems surprised and happy to see us, but can't maintain anything for long since he's only breathing every other 30 seconds. The dog won't go near the bed, just like before; I think the bars on the sides frighten her. The hospice nurses are friendly like last time, and we set in to wait.

The next day, he still spends half the time struggling for breath and the other half not breathing. The few times he manages to open his eyes or speak, he tries to stand up, tries to leave, but he's just not strong enough. We keep things quiet around his house, we try to make him comfortable and greet him when he wakes up. People keep telling him it's okay if he dies, but they refuse to use those words. I hope he stops suffering soon. Before we leave, he is struggling and saying something about "alone". We stay for a little longer, but he continues, so we leave. My sister thinks he's lonely, I think he wants to be left alone. The dog doesn't want to leave the house. The nurses start talking about how she can tell that he's dying, I think she can tell that we can tell he's dying. I have to drag her to the car so we can go back to the hotel.

The next day, he's barely able to open his eyes at all. He doesn't speak even for the brief periods he appears conscious, and the breathing he's doing for half of each minute is shallower than before. I expect he won't survive the day, but I say nothing. Everyone around is clearly getting more agitated about the situation. My mother is getting sadder, and one of the nurses tries to make her feel better by relating a near-death experience from one of her friends, but I say nothing. People continue to tell him that it's okay for him to die, still only using euphemisms, except for one nurse who thinks he's going to some vague spirit-realm to be with my grandmother. I can't tell if she's speaking literally or metaphorically, but I say nothing.

He's looking more gaunt all the time, like his skin is draped over his skull. I begin to wonder about what's happening to his body - I am plagued by the worry that he recovered from his illness and we are starving him to death in ignorance, but I say nothing. We are told that he may feel better if he hears life continuing around him as normal, so we try. Eating dinner in the next room, I wonder if the smell of food is making him feel worse for hunger, but I say nothing. He wakes up for long enough to take his oxygen tube off in front of everyone, I am amazed he still has the strength. In the evening we leave, the nurse telling us that he's unlikely to survive for more than a few hours. My grandmother died soon after everyone went to sleep, so I spend the rest of the evening expecting a phone call saying he had died.

The next day we arrive to a new experience - he is breathing consistently now, but it sounds like coffee loudly percolating in his lungs with every breath. The nurse assures us that it's not unpleasant for him, only for us. I sit in the rocking chair in the room with him, programming on my laptop. Rocking back and forth, expressionless, silent. I ignore more talk about him being with my grandmother soon. Nobody else wants to be in the room with him for very long, I think the noise of his breathing is the reason. After four hours, it's getting to me too. I begin getting angry at the world for making physician-assisted suicide such a taboo, but I say nothing.

In the afternoon, his breathing gradually slows until eventually it stops entirely. A minute later, he gasps another breath, everyone is surprised, but the nurse says it's just a muscle spasm, that he's gone now. People around are crying, I keep staring at his face. A couple minutes later he gasps for another breath, weaker than last time. Other people don't seem to notice this time. He doesn't breathe again, and his head stops moving to the rhythm of a pulse, which I assume means his heart has stopped. I continue to stare at his face for another ten minutes or so, and I say nothing.

The next few days, everyone is bustling around cleaning, throwing things out, rummaging through his posessions, planning his funeral, trying to figure out how to proceed from here - working through grief by immersion in work, I assume. I help when asked, but otherwise I sit out of the way, programming or solving logic puzzles, just as the days before. I continue to be angry at the world for not allowing physician-assisted suicide, but also I know that he would probably not have taken it even if it were legal. I reconcile this by also being angry at the culture for its social disapproval of the practice, but I say nothing. The uninterrupted noise eventually gets to me, and once I use a volume of voice normally reserved for getting the attention of a large lecture hall. I am briefly chastised for this, and I wonder why I must give leeway to everyone else's methods for dealing with grief though they need not accommodate mine, but I say nothing.

In the calling hours before his funeral, people apologize a lot, people hug a lot, people shake hands a lot. I stand when they do, shake hands when the offer, and sometimes introduce myself. One nurse talks about how my grandparents have new bodies now and are probably sitting on the couch listening to music and tapping their feet and hands. I scream at her in my mind about a hundred different things, but I say nothing.

The funeral starts with a sermon. My grandfather is mentioned twice, the rest is about "Christ Jesus" and "Resurrection" and "Almightly Lord God". Every time she says "will you pray with me?" I mentally reply "NO!" but I say nothing. When the minister closes the bible on the podium, she opens up the notes she took when talking to us a couple of days earlier, and reads them out with a little bit of a filter and almost no editorializing. I wonder why she is even here, but I say nothing. My sister reads the lyrics of a song she finds appropriate to my grandparents, and it is all I can do not to cry - this short, abnormal part of the service is more moving than all the rest put together. The minister finishes with another prayer. Through the entire thing I keep repeating that I am not there for myself, I am there for the rest of my family - they think I would feel badly for not being there. They are wrong, but I say nothing.

We go to the cemetery to inter his ashes. We pick up the dog on the way, hoping she will behave herself there, it turns out she doesn't. After another meaningless prayer, we leave the cemetary. We eat out that night, at a favourite restaurant of my grandfather's.

The next morning, my sister and I board the bus to leave. She remarks that it's a rare thing for someone to die in the house they built. For the first two hours, a man sits behind me speaking very loudly about his friend across the aisle being released from prison recently, and about meeting someone in a casino. I do my best to ignore him. The second two hours, after a bus transfer, a woman sits behind me screaming constantly with her friend across the aisle about their lives, completely oblivious to others on the bus, and never stopping for a breath even when her friend is speaking. She is even more difficult to ignore. Thankfully, the third two hours are relatively silent. Two more hours of local travel later, and I am finally back to my room in Hamilton after 8 days away.

Two days after my return, I can finally begin to grieve for my grandfather. I am glad he's not suffering anymore, but I will miss him.

Sunday, December 6, 2009

What to do with multiple OpenIDs?

The ability to have a single online identity is a worthwhile goal, in my opinion, and OpenID seems to be a major step in that direction. It allows login to any OpenID-enabled website through the use of your single identity, and tools like Verisign's Seatbelt make that even simpler. I'm quite pleased to see that more and more websites are adopting OpenID as a means of signing up or signing in.

The question I have now is: What do I do with multiple OpenID accounts?

Since more websites are using OpenID, more of them are also making their existing users able to use their existing logins as OpenIDs. This means that I already have at least 3 OpenIDs and no way to consolidate them.

This might seem like it has an easy solution - simply stop using two of them. The problem is that the one I've been using most already isn't the Google one, since Google's change to OpenID is more recent - and starting a new account on Google with my favoured OpenID would require too many transfers of data and notifications of third parties to be worth it.

So basically, I am looking for a way to use one of my OpenIDs to absorb the existing permissions and accounts of the others.

Monday, September 7, 2009

Discordian Poe

For those of you unfamiliar with Poe's Law, I recommend you take a look at this link, because I am about to turn it completely inside out.

Every religious, spiritual, and/or mystical belief has equal validity, including the belief that this equality is a joke.

Hooray for fundamentalist Discordianism!

Monday, August 31, 2009

Pure Intentions, Or Why I Dislike Networking

When I say "networking" as in the title of this post, I am talking primarily about the way people in the professional world make and use acquaintances as part of their jobs.

Almost every job on the planet benefits from networking - making personal connections with people who can help you out in your work. Almost every job needs at least some degree of networking to function, and it can be very difficult to get a job in the first place without knowing at least some of the right people - a resumé and a good interview are usually trumped by a personal recommendation. All of this makes very good psychological sense as well, since we are a social species who evolved in relatively small, insular communities (in comparison with the modern world, that is).

But I don't like it.
I idealistically think that the person who gets the job should be the person who can best do the job, not the person who is being recommended by someone closest to the employer. As far as I can tell most people agree with this sentiment, at least superficially.

I am not a very socially capable person. I accept that social situations are not my natural environment, and I have put significant effort into gaining what little skill I have at present. I am never going to be a politician, or a talent agent, or a sales representative.

There are many jobs for which it makes good sense to require a high degree of social skill, and there are many jobs whose content largely is networking itself. In these cases it would be ludicrous to attempt to remove networking requirements to obtaining the job.

Even in academia, my chosen direction, a certain degree of networking is sensible to have should one desire recognition or a position with administrative duties.

But networking itself, when not in a job which explicitly involves it, seems disingenuous and distasteful to me.

When making a new friend, most people won't immediately consider how the friendship could benefit their career - that's considered a form of using the person.
There is clearly a difference between making a friend so that they will be useful, and making a friend who later happens to be useful. Right?

The ways in which a person could be useful in furtherance of one's own goals are usually fairly simple and easy to see. As such, we don't even have to consciously recognize potential uses in order for them to be considered in our decision-making process. These considerations are likely to result in biases through which people make friends with people who are likely to be useful in future, without the moral penalties associated with doing this consciously.

Here's where the problem comes in: reasonable expectations of knowledge, even in retrospect, should apply to present considerations.

In more detail, when considering whether or not asking a favour of a friend "counts as using them" in an inappropriate sense, we should take into account what we would reasonably have known throughout the prior relationship, even if we don't have a particular memory of recognizing that knowledge.

For example, if I ask a friend of mine to help me with my computer, I should take into account the fact that I knew he was a software engineer when we first met, even though I didn't specifically think at the time of him helping solve my computer problems.

Seen carefully, this results in my preference for paying a stranger to do a job over having a friend do it for free.

Oddly, none of this presents any barriers to my doing things to help the careers of my friends, but this is simply another situation where I find it morally unpleasant to accept reciprocation, for the simple reason that it is morally distasteful to expect it.

Friday, June 5, 2009

Rights of the Individual vs. Rights of the Individual

It is a staple of science fiction to tell a tale in which artificial intelligences must struggle to attain equal rights with humans. It is also commonplace to recognize that, if a human being uploads their consciousness to a machine, the rights are carried with that consciousness.

People find it much easier to accept that an artificial intelligence deserves rights when that intelligence inhabits a body. This is, of course, a natural by-product of the way our brain interprets other humans as moral agents - our moral sense evolved to recognize other humans as deserving of rights.

When speculating about a consciousness being uploaded from its originating human body to a machine, we usually assume that either the body is then rendered effectively comatose (a shell or doll, so to speak) thus removing moral obligations to the body, or we assume that the consciousness is copied to the machine while also remaining in the body, creating two beings each deserving of moral consideration.

I would like to consider the former situation - suppose that a human consciousness is uploaded to a machine and the body then retains its neural ability to regulate breathing, heartbeat, and other unconscious brain functions, but does not keep memories or even acquired skills. Is the body then truly no longer deserving of moral consideration?

Shouldn't we then treat this body as a somewhat comatose individual? In this case, this "uninhabited" body may very well relearn motor skills and language as an infant would (alright, neuroplasticity in adults is much lower than in infants, so it could relearn these things as a developmentally challenged infant would), then it might proceed to develop another new personality. Should we dismiss this possibility outright and simply treat this body as a shell?

I think these ideas certainly merit consideration, but are highly unlikely to be resolved until such time as we actually develop some form of consciousness-uploading technology.

Additionally, the primary source for my thinking about these ideas is the series Dollhouse which, near the end of season 1, poses the question of whether or not the mind has an obligation to the body.

Clearly, of course, all this presupposes that mind and body are, in fact, separable in some meaningful sense, which I believe to be a reasonable idea but clearly not yet supported by evidence.

Wednesday, January 28, 2009

An Interesting Example of Foresight

I sat in the audience at a recent religious discussion panel and had the good fortune to share conversations with two of the panelists after it had finished. Both panelists (the Muslim and Christian panelists), when questioned about why they believed (or why I should believe) presented practically identical variations of the first cause argument.
While I think that the standard response to the first cause argument (where did God come from, then?) is all well and good, I prefer to rely on my own brand of confusing weirdness - a sort of mathematical argument that even though the universe has a finite age, there does not need to have been a first instant of time, and hence no first cause is needed. Additionally, I like to object to the prohibition on infinite causal chains and to the crucial separation of cause from effect in the early universe, but this time I focused on time as a spatial dimension and so (possibly) finite but unbounded.
The difficulty with this argument, as I said explicitly several times during these conversations, is that it dispatches nicely with the question of a first cause, but it proposes no answer to the question of "why is there something rather than nothing?" - the best formulation I have yet heard for the idea apparently being pondered.
I was surprised, however, that both panelists seemed extremely resistant to the question being phrased in this fashion. It makes sense for them to resist it, since "God" is a clearly unsatisfying answer to this phrasing, presumably being a "something" himself, but I find it distasteful to think that the panelists had seen this consequence of the phrasing and consciously resisted it. Instead, I am left with the puzzle whereby, if they were being honest and candid about their thoughts, why would they have refused such a clear restatement of the question at hand?